Iraqi Journal of Chemical and Petroleum Engineering Vol.16 No.4 (December 2015) 51- 58 ISSN: 1997-4884 Density, Viscosity and Refractive Index of the Ternary System (Ethanol + N-Hexane +3-Methyl Pentane) at 20, 30, 40 ° C and 101.325 Kpa Ghazwan A. Mohammed * and Maryam Kh. Oudah * Chemical Engineering Department-College of Engineering-University of Baghdad-Iraq Abstract Experimental densities, viscosities η, and refractive indices nD data of the ternary ethanol+ n-hexane + 3-methyl pentane system have been determined at temperatures 293.15,303.15 and 313.15 K and at atmospheric pressure then these properties were calculated theoretically by using mixing rules for densities, viscosities and refractive indices .After that the theoretical data and the experimental data were compared due to the high relative errors in viscosities an equation of viscosity was proposed to decrease the relative errors. Key Words: Thermodynamic properties, Measuring, Viscometer, Pycnometer , Refractive indices. Introduction Prediction of the thermodynamic properties of materials associated with the process can greatly affect the design, cost, and in some cases even determine the feasibility of a given unit operation. The need for accurate values of thermodynamic properties of an increasing variety of materials to support the design of processes places a strong emphasis on the development of techniques with predictive capabilities that can be used for a wide range of process conditions and mixtures with limited reliance on experimental data beyond that used at the early stages of the process development [1]. In such regard, thermodynamic and transport properties of fluid mixtures are required that might sometime obtained from tables but it is usually found that even the most extensive physic-chemical tables do not contain all the data necessary for designing a technological process. In such cases, properties have only been studied for pure components from which the mixture is constituted where method is required for estimating the properties of the mixtures. Such predictions usually entail large difficulties [2]. Finally, Properties alone remain elusive; failure to reach this goal as follows from an inadequate fundamental understanding of liquid structure and intermolecular forces. All macroscopic properties are related to molecular structure, which determines the magnitude and predominant type of the intermolecular forces [3]. Iraqi Journal of Chemical and Petroleum Engineering University of Baghdad College of Engineering Density, Viscosity and Refractive Index of the Ternary System (Ethanol + N-Hexane +3-Methyl Pentane) at 20, 30, 40 ° C and 101.325 Kpa 52 IJCPE Vol.16 No.4 (Dec. 2015) -Available online at: www.iasj.net Experimental Section 1- Materials Ethanol, n-hexane and 3-methyl pentane were used in preparing the binary and ternary systems studied and acetone was used for cleaning the glassware were all purchased from Sigma and Thomas Baker with purity over 99%. Table 1 lists values of the properties of chemicals used in this study given by literature [4]. Table 1, Densities (ρ), Viscosities (η), and Refractive Indices (nD) of Pure Compounds Used in This Work Compared with Literature Data at t = 20 o C, t = 30 o C and 40 o C at atmospheric pressure t = 20 o C Compound ⍴ / g.Cm -3 η /mpa.s nD Exp. Lit. Exp. Lit Exp. Lit. Ethanol 0.7895 0.790(75) 1.247 1.184(79) 1.3618 1.3618(79) n-hexane 0.6480 0.655(34) 0.364 0.301(27) 1.3718 (98) 1.376 3-methyl pentane 0.659 0.6537(15) 0.301 0.292(41) 1.376 1.376(98) t = 30 o C Ethanol 0.7702 0.7709(76) 1.1514 0.997(79) 1.3600 --- n-hexane 0.64078 0.651(15) 0.3280 0.2956(79) 1.3730 --- 3-methyl pentane 0.659 0.65369(15) 0.2674 0.263796(41) 1.3714 --- t = 40 o C Ethanol 0.7614 0.7728(76) 0.8742 0.793(76) 1.3574 --- n-hexane 0.63118 0.6411(77) 0.29681 0.2537(79) 1.3695 --- 3-methyl pentane 0.6435 0.6440(15) 0.2357 0.2398(41) 1.3689 --- 2- Measurements Densitie ρ measurements were measured, by pycnometer, while viscosity and refractive index measurements were made by using the Cannon-Fenske routine viscometer and refractometer respectively. Results and Discussion 1- Density The densities of the pure components ethanol and n-hexane were calculated using equations (1) and (4) respectively, while the density of pure water was determined by using equation (5). As for the density of pure component 3-methyl pentane equation (9) was used. ⍴ ⍴ ⍴ * ( ) ( ) + ... (1) Po = 0.1013 MPa Where : ρo = ρ c {1 + ∑ (1-Tr) (i/3) } ... (2) And = 331.2083 - 713.86 Tr + 401.61 Tr2 – F ... (3) For ethanol: = 520.23 -1240 Tr + 827 Tr 2 – F ... (4) Ghazwan A. Mohammed and Maryam Kh. Oudah -Available online at: www.iasj.net IJCPE Vol.16 No.4 (Dec. 2015) 53 For water: ⍴ = 999.84 + 0.053 (T- 273.15) – 7.315*10 -3 (T-273.15) 2 +3.03*10 -5 (T-273.15) 3 ... (5) For 3-methyl pentane using equation (6): = VR (0) [ 1 - WSRK VR (δ) ] ... (6) Where: VR (0) = 1+ a [1- Tr] (1/3) + b (1-Tr) (2/3) + c (1-Tr) + d (1-Tr) (4/3) ... (7) 0.25 < Tr < 0.95 And VR (δ) = ( – ) ... (8) 0.25 < Tr < 1.00 For, Tc obtained from table 2. Table 2, pure component parameters for The Hankinson-Brobst- Thomson and The Rackett Liquid volume correlations 3-methyl pentane V* (L /mol) WSRK Pc (bar) Tc (K) 0.3633 0.2741 31.2 504.34 The values of the constants in equations above are: a = -1.52816 , b =1. 43907, c = - 0.81446 , d = 0.190454 e = -0.296123 , F = 0.386914, g = - 0.0427258, h = - 0.0480645. As listed in table 2 V* is a pure component characteristic volume generally within 1 to 4 percent of the critical volume, WSRK is the acentric factor which forces the Soave equation to give a best fit, of existing vapor pressure data. Values of V* and WSRK are given in table 2 [ 5, 6 , 7 ].Thomson et all have extended the HBT method to allow prediction by generalizing the constants in the Tait equation [ 7 ], Thus : V = Vs (1- c Ln ) ... (9) Where Vs is defined as the saturated liquid volume at the vapor pressure Pvp , which obtained from equation (6). The rest of the parameters , and c are obtained from as illustrated below in equations 10, 11, 12 and 13: / PC = -1 + a (1- Tr) (1/3) + b (1- Tr) (2/3) + d (1- Tr) + e (1- Tr) (4/3) ... (10) Where [3] Ln ( /Pc) = (1-x) -1 [(VPA) x + (VPB) x 1.5 + (VPC) x 3 + (VPD) x 6 ] ... (11) X = 1- ... (12) Values of VPA, VPB, VPC and VPD are given in table 3. Table 3, Vapor Pressure, in bars 3-methyl pentane VPD VPC VPB VPA -2.17642 -2.81741 1.26113 -7.27084 e = exp (f + g wsRK + h w 2 sRK) … (13) And c = j + k wSRK ... (14) a = - 9.070217 , b = 62.45326, d = -135.1102 , f = 4.79594, g = 0.250047 , h = 1.14188, j = 0.0861488 , k = 0.034483 Density, Viscosity and Refractive Index of the Ternary System (Ethanol + N-Hexane +3-Methyl Pentane) at 20, 30, 40 ° C and 101.325 Kpa 54 IJCPE Vol.16 No.4 (Dec. 2015) -Available online at: www.iasj.net Equation (15) applied to ternary system to calculate the density for the ternary system (ethanol +n-hexane +3- methyl pentane): ⍴mix = w1 * ⍴1 + w2* ⍴2 + w3* ⍴3... (15) Where ⍴1, ⍴2, ⍴3 were the densities of pure component 1, 2, 3 and w1, w2 , w3 were the weight fractions of component 1,2,3. ( ( ) ) ... (16) The density of the ternary system ethanol (1) + n-hexane (2) + 3-methyl pentane (3) was calculated using the pure density of each component and the weight fraction and equation 15. The results were compared with experimental values by calculating the % relative error (%Er) given by equation 16. Table 4 lists the results of the comparison at 20 o C while table 5 and 6 lists values at 30 o C and 40 o C respectively. Table 4, Density (⍴) of ternary system, ethanol (1) + n-hexane (2) + 3-methyl pentane (3) at different weight fractions of ethanol (Wt.1) at temperatures 20℃ %Er ⍴ equ. (15) ⍴ exp. Wt.2 Wt.1 1.10 1.50 1.62 1.61 2.07 2.04 2.19 2.06 0.28 1.61 0.6552 0.6743 0.6771 0.6810 0.7045 0.7175 0.7271 0.7483 0.7873 Average 0.6480 0.6643 0.6663 0.6702 0.6902 0.7031 0.7116 0.7331 0.7895 0.950 0.813 0.793 0.765 0.595 0.502 0.433 0.281 0.000 0.00000.1 45 0.166 0.195 0.374 0.472 0.545 0.705 1.000 Table 5, Density (⍴) of ternary system, ethanol (1) + n-hexane (2) + 3-methyl pentane (3) at different weight fractions of ethanol (Wt.1) at temperatures 30℃ %Er ⍴ equ.(15) ⍴ exp. Wt .2 Wt .1 0.84 1.74 1.67 2.12 2.85 2.08 1.91 1.37 1.10 1.63 0.6461 0.6653 0.7200 0.6956 0.7086 0.7183 0.7395 0.7571 0.7787 Average 0.6408 0.6539 0.6610 0.6812 0.6890 0.7037 0.7257 0.7543 0.7702 0.950 0.813 0.765 0.595 0.502 0.433 0.281 0.155 0.000 0.000 0.145 0.195 0.374 0.472 0.545 0.705 0.837 1.000 Table 6, Density (⍴) of ternary system, ethanol (1) + n-hexane (2) + 3-methyl pentane (3) at different weight fractions of ethanol (Wt.1) at temperatures 40℃ %Er ⍴ equ. (15) ⍴ exp. Wt.2 Wt.1 0.92 2.01 2.11 2.53 2.50 2.30 2.12 1.13 1.95 0.6370 0.6561 0.6651 0.6892 0.7016 0.7097 0.735 0.7700 Average 0.6312 0.6431 0.6514 0.6722 0.6846 0.6937 0.7163 0.7614 0.950 0.813 0.749 0.577 0.488 0.431 0.275 0.000 0.000 0.144 0.212 0.393 0.486 0.547 0.711 1.000 2- Viscosity The viscosity values for the pure components and the ternary system was measured. The viscosity of pure components ethanol and n-hexane was calculated from equation (17) while viscosity of water was calculated by using equation (18), and finally the viscosity for 3-methyl pentane was determined by using equation (19). η* = ( ) (2 NA) (1/3) π (1/2) ( ) (1/2) ( η ( ) ) ... (17) Ln η =A +B/T +C* T +D*T 2 ... (18) Ln ... (19) Ghazwan A. Mohammed and Maryam Kh. Oudah -Available online at: www.iasj.net IJCPE Vol.16 No.4 (Dec. 2015) 55 Where ηL=Liquid Viscosity, in Cpand ⍴L is the iquid density at 20 C in g/cm 3 . M is the molecular weight in g/mole and T is the temperature in K and the constants A and B are given in table 7 [ 8 ]. Table 7, the parameters of Orrick and Erbar method 3-methyl pentane B A 275+ 99n -(6.95 + 0.21n) 35 -0.15 When n = the carbon number. Fig. 1, The data given in tables 6, 7 and 8 are plotted as viscosity verses weight fraction at temperatures t = 20 o C , 30 o C and 40 o C Figure (1) shows the experimental values of viscosity as plotted versus weight fraction of ethanol for ternary system it was noted the increase in the value of viscosity as weight fraction of ethanol increases in such respond, we proposed an equation that involves the use of activity coefficients as shown in equation (20) for determination of viscosity values in ternary system. η = A* ηmix * ( ) B ... (20) ηmix is defined by equation (21),and ϓ1 and ϓ2 known as activity coefficients of component 1 and 2 determined from Wilson model. While A, ηmix and B are determined from following equations. ηmix = w1 * η1 + w2* η2 + w3* η3... (21) A= (ρ ρ ) (ρ ρ ) ... (22) B= ( ) ... (23) Where ρc is the critical density of a component. When equation (20) was applied on the above ternary system the relative errors have been reduced as noticed in tables 8, 9 and 10. Table 8, Viscosities (η) of the ternary system ethanol (1) + n-hexane (2) + 3-methyl pentane (3) at different weight fractions of ethanol (Wt.1) at temperature of 20 o C determined using equation (20). Er% η exp. η equ 20 ϓ2 ϓ1 Wt.2 Wt.1 25.48 8.92 9.49 2.69 5.34 2.65 2.04 14.86 5.19 0.3645 0.4285 0.4497 0.4423 0.6039 0.6328 0.6938 1.2473 Average 0.2716 0.3903 0.4070 0.4304 0.5717 0.6496 0.7079 1.0747 1.000 1.231 1.278 1.346 1.851 2.203 2.506 5.584 19.428 2.648 2.387 2.114 1.379 1.221 1.146 1.000 0.950 0.813 0.793 0.765 0.595 0.502 0.433 0.000 0.000 0.144 0.166 0.195 0.373 0.471 0.545 1.000 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 E x p e ri m e n ta l V is co si ty ( cp ) Weight fraction of ethanol (1) t = 20c t = 30c t = 40c Density, Viscosity and Refractive Index of the Ternary System (Ethanol + N-Hexane +3-Methyl Pentane) at 20, 30, 40 ° C and 101.325 Kpa 56 IJCPE Vol.16 No.4 (Dec. 2015) -Available online at: www.iasj.net Table 9, Viscosities (η) of the ternary system ethano (1) + n-hexane (2) + 3-methyl pentane (3) at different weight fractions of ethanol (Wt.1) at temperature of 30 o C determined using equation (20). Er% η exp. η equ 20)) ϓ2 ϓ1 Wt.2 Wt.1 26.90 4.41 1.62 8.66 6.28 7.48 3.33 6.87 14.48 5.57 0.328 0.363 0.377 0.468 0.544 0.586 0.722 0.904 1.151 Average 0.239 0.347 0.383 0.509 0.578 0.630 0.746 0.842 0.963 1.000 1.270 1.400 1.996 2.447 2.866 4.143 5.808 9.322 40.38 3.078 2.411 1.502 1.302 1.205 1.075 1.022 1.000 0.950 0.813 0.765 0.595 0.502 0.433 0.281 0.155 0.000 0.000 0.145 0.195 0.374 0,472 0.545 0.705 0.837 1.000 Table 10, Viscosities (η) of the ternary system ethanol (1) + n-hexane (2) + 3-methyl pentane (3) at different weight fractions of ethanol (Wt.1) at temperature of 40 o C determined using equation (20). Er% η exp. η equ 20 ϓ2 ϓ1 Wt.2 Wt.1 23.82 4.68 0.84 6.72 2.69 0.42 0.84 14.48 2.70 0.2968 0.3208 0.3434 0.4055 0.4682 0.5140 0.6022 0.8742 Average 0.2261 0.3058 0.3405 0.4328 0.4808 0.5119 0.5972 0.7515 1.000 1.261 1.437 2.061 2.506 2.854 4.158 9.149 35.553 3.078 2.254 1.451 1.277 1.201 1.071 1.000 0.950 0.813 0.749 0.577 0.488 0.431 0.275 0.000 0.000 0.144 0.212 0.393 0.486 0.547 0.711 1.000 3- Refractive index The refractive index of the ternary system ethanol (1) + n-hexane (2) + 3- methyl pentane (3) was calculated from pure component data by using equation (23) and using the volume fraction via equation (24). nD = [ 1 + φ1 ( nD1 2 – 1) + φ2 ( nD2 2 – 1) + φ3 ( nD3 2 – 1)] (1/2) … (23) φi= ... (24) It seemed as pointed out in table 1 the experimental data of pure compounds obtained in the present study are in good agreement with their corresponding literature values. Tables 11, 12 and 13 lists the refractive index of the ternary system determined from above equation and compared with experimental values at 20 0 C, 30 0 C, 40 0 C. Ghazwan A. Mohammed and Maryam Kh. Oudah -Available online at: www.iasj.net IJCPE Vol.16 No.4 (Dec. 2015) 57 Table 11, Refractive indices (nD) of the ternary system ethanol (1) + n-hexane (2) + 3- methyl pentane (3) at different weight fractions of ethanol (Wt.1) and at 20℃ by using equation (23) Er % nD exp. nD mix. φ 2 φ 1 Wt.2 Wt.1 0.031 0032 0.026 0.037 0.034 0.026 0.000 0.027 1.3725 1.3720 1.3718 1.3702 1.3682 1.3658 1.3600 Average 1.3729 1.3724 1.3721 1.3707 1.3686 1.3661 1.3600 0.950 0.834 0.792 0.636 0.476 0.317 0.000 0.000 0.125 0.171 0.337 0.506 0.672 1.000 0.950 0.813 0.765 0.595 0.433 0.281 0.000 0.000 0.145 0.195 0.374 0.545 0.705 1.000 Table 12, Refractive indices (nD) of the ternary system ethanol (1) + n-hexane (2) + 3- methyl pentane (3) at different weight fractions of ethanol (Wt.1) and at 30℃ by using equation (23) Er % nD exp. nD Mix. φ 3 φ 2 φ 1 Wt.2 Wt.1 0.015 0.048 0.076 0.025 0.097 0.034 0.027 0.000 0.04 1.3718 1.3715 1.3710 1.3708 1.3690 1.3670 1.3650 1.3618 Average 1.3720 1.3722 1.3720 1.3711 1.3703 1.3675 1.3654 1.3618 0.000 0.044 0.041 0.033 0.028 0.017 0.010 0.000 0.950 0.838 0.782 0.624 0.537 0.315 0.187 0.000 0.000 0.123 0.183 0.352 0.444 0.675 0.808 1.000 0.950 0.813 0.749 0.577 0.488 0.275 0.159 0.000 0.000 0.144 0.212 0.393 0.486 0.711 0.832 1.000 Table 13, Refractive indexes (nD) of the ternary system ethanol (1) + n-hexane (2) + 3-methyl pentane (3) at different weight fractions of ethanol (Wt.1) and at 40℃ by using equation (23) Er % nD exp. nD mix. φ 2 φ 1 Wt.2 Wt.1 0.034 0.049 0.061 0.037 0.053 0.027 0.047 0.000 0.038 1.3690 1.3687 1.3683 1.3674 1.3662 1.3658 1.3630 1.3574 Average 1.3695 1.3694 1.3691 1.3679 1.3669 1.3662 1.3636 1.3574 0.950 0.838 0.782 0.624 0.537 0.479 0.315 0.000 0.000 0.123 0.183 0.352 0.444 0.504 0.675 1.000 0.950 0.814 0.749 0.577 0.488 0.431 0.275 0.000 0.000 0.144 0.212 0.393 0.486 0.547 0.711 1.000 Density, Viscosity and Refractive Index of the Ternary System (Ethanol + N-Hexane +3-Methyl Pentane) at 20, 30, 40 ° C and 101.325 Kpa 58 IJCPE Vol.16 No.4 (Dec. 2015) -Available online at: www.iasj.net Conclusion The collected experimental data for the densities and the refractive indices of the ternary system are in good agreement with the theoretical data. Because of close matching between experimental and theoretical data we found there is no need to propose new correlation for the determination of density and refractive index for predicting ternary system from pure component data. While for the viscosities of the binary and ternary systems, the relative errors were high so a new correlation was. The new proposal gave good results and could be suitable for liquid solutions. Nomenclature %Er: Relative error ⍴: Density at T and P ⍴ : Density at To and Po ⍴c: Density at Tc and Pc ABS: Absolute value Ai: Constant in equation 2[9] B: Pressure correction in equation 3: F: Constant in equation 3 NA: Avogadros constant nD: Refractive index of mixture nDi: Refractive index of component i PC: Critical pressure Po: Reference pressure Pve: Vapor pressure R: Universal gas constant T: Temprature TC: Critical temperature Tr: Reduced temprature V: volume Vm: Molar volume VR(0): Reduced volume defined by equation 7 VR(δ): Reduced volume defined by equation 8 VS: Volume at saturation wi: Weight fraction of component i WSRK: Acentric factor Z: Coordination number[9] : Pressure term in equation 10 η: viscosity ηmix: Viscosity of mixture π: pi ρmix: Density of mixture ϓi: Activity coefficient of component i References 1- Dohrn, R.; Pfohl, O. Thermophysical properties – Industrial directions. Fluid Phase Equilib. 2002, 194−197, 15−29. 2- Giro, F. ;Goncalves, M. 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V. ,(1971)," Prediction of Transport and Other Physical properties of Fluids " , Pergamon Press, Oxford. 9- Marc J. Assael, J. P. Martin Trusler and Thomas F. Tso akis, (1996),” Thermophysical Properties of Fluids an Introduction to Their Properties”, Imperial College Press, London.